268 Mr. G. H. Darwin. [Mar. 18, 



Fig. 2. 



Diagram for Obliquity of Planet's Equator. — First case. 



As a special example of this we see that, if the obliquity be zero at 

 any point, a consideration of the curve will determine whether zero 

 obliquity be dynamically stable or not ; for if the arrows on the curve 

 of obliquity be approaching the axis of as, zero obliquity is dynamically 

 stable, and if receding from the axis of x, dynamically unstable. 



Hence from x= + oo to B, zero obliquity is dynamically unstable, 

 from — oo to and A to dynamically stable, and from A to B, first 

 stable, then unstable, and finally stable. 



The infinite value of the obliquity at the point B has a peculiar 

 significance, for at B the planet has no rotation, and being thus free 

 from what Sir William Thomson calls "gyroscopic domination," the 

 obliquity changes with infinite ease. In fact at B the term equator 

 loses its meaning. The infinite value at A has a different meaning. 

 The configuration A is one of maximum energy and of dynamical 

 equilibrium, but is unstable as regards mean distance and planetary 

 rotation ; at this point the system changes infinitely slowly as regards 



